Can I apply polyurethane over paint?

Is it ok for me to apply polyurethane over a painted wall so that I can protect it? I painted my wall in the bathroom what turns out to be a flat yellow. I love the color, it’s great (IMO), and it’s almost new paint, but it already has marks from various objects leaning on it, etc. So I’m thinking to cover over quite a bit of it with clear semi-gloss. What do you think?
—
Absolutely. And you can get flat, semigloss or gloss for the finish you want. Also, you should get water-
base.
—
OK, since you are going to buy paint ( poly ) any way, why don’t you just get the yellow color you like mixed up in a semi-gloss enamel( one specifically for high moisture areas, they have anti-mold and fungicides in them already), and repaint the bathroom.
—
The reason is that I already put the paint on the walls. And I don’t know what color it is, but that is besides the point since most of it is done. I see so many patches I need to clear up, this is worse than I thought it would be. But thank you for your suggestion. I mixed a lot of colors, not knowing what I was doing, and came up with this color that I like very much. there is not much left of it (I got scared when I saw how little is left of it, but I have almost the small room done…sigh of relief). I know I can get a color match in a good paint store, but I hope that won’t be necessary. Now I have another question which I will post in another message. Thanks again, you all have been so helpful. But back to the point you bring up. Were you saying that if I get paint in the future and want a washable surface, that I should have the people mix it with a can of semi-gloss clear?
—
Well, I painted my cabinets with enamel, but then painted some of the trim with the latex paint that matched very well. I can see maybe I should have put the enamel on it instead. This is hard. tedious. Well, anywayyy…can I paint over the latex acrylic or whatever the mix is with enamel and get a smooth enough surface? whatchooall think?
—
I put poly over paint on my bathroom walls, also vanity top which I covered with wallpaper… Just remember to use satin or semi gloss or else it will look shiny.